Nonlinear Price Impact and Portfolio Choice
31 Pages Posted: 2 Jun 2015 Last revised: 16 May 2018
Date Written: June 2, 2015
In a market with price-impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long-term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price-impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square-root impact law and, as extreme cases, linear impact and proportional transaction costs.
Keywords: price-impact, square-root law, trading volume
JEL Classification: G11, G12
Suggested Citation: Suggested Citation